Entropy properties of deterministic control systems

The purpose of this tutorial paper is to explain and to survey a number of concepts and results for deterministic control systems centering on the problem to determine the “information” needed for performing control tasks. Entropy theory of dynamical systems provides a guideline in the sense that the developments for control systems are seen, sometimes in analogy and sometimes in contrast, to those for dynamical systems. A focus will be on the problem to keep a subset of the state space invariant. Furthermore, a number of open problems in this field will be elucidated.